Manuscript VI@1 · VI.tex · section · b5b60afb

Formal solution jets

Action, signs, background, and coefficient domain › Formal solution jets · lines 427–454

VI@1#eq:jets, VI@1#eq:wave-expansion

Work coefficientwise modulo $κ^{3}$ , and write

γ = η + κh + κ^{2} j, ϕ = ϕ_{0} + κ ϕ_{1} + κ^{2} ϕ_{2} .

Define $G^{(2)} [h, h]$ by

G (η + κh + κ^{2} j) = κ G^{(1)} (h) + κ^{2} (G^{(1)} (j) + G^{(2)} [h, h]) mod κ^{3} .

Similarly, define $M_{h}$ by

□_{η + κh + κ^{2} j} - m^{2} = P + κ L_{h} + κ^{2} (L_{j} + M_{h}) mod κ^{3} .

An explicit formula for $M_{h}$ is given in Section sec:scalar-expansion.

Displayed formulas in this passage

VI@1#eq:jets · line 430
$γ = η + κh + κ^{2} j, ϕ = ϕ_{0} + κ ϕ_{1} + κ^{2} ϕ_{2} .$
VI@1#eq:wave-expansion · line 445
$□_{η + κh + κ^{2} j} - m^{2} = P + κ L_{h} + κ^{2} (L_{j} + M_{h}) mod κ^{3} .$
unlabeled · line 437
$G (η + κh + κ^{2} j) = κ G^{(1)} (h) + κ^{2} (G^{(1)} (j) + G^{(2)} [h, h]) mod κ^{3} .$